Excellence in Research: Mathematical Analysis of the Prevention of HIV with PrEP and HAART Treatment

Howard University, Washington DC

Investigators

Abstract

Prevention, mitigation, and eradication of HIV has been the focus of governments, scientists, and public health professionals for decades. Recent reports, such as the “Ending the HIV Epidemic: A Plan for America” distributed by the US Department of Health and Human Services, have generated a renewed hope for the millions of people around the world affected by this disease. To achieve this goal, it is imperative to understand the most effective use of available resources in light of the new prophylaxis treatment and the continued improvements of the highly active anti-retroviral treatment, particularly in the case of non-compliance. A realistic mathematical model, including these two treatments, as well as disproportional effects on disparate subpopulations, is essential for effective resource utilization. The broader impacts of this proposal are far-reaching from a public health perspective, but will also serve as a platform to train primarily underrepresented undergraduate and graduate students at the interface of mathematics and medicine. This collaboration between researchers at Howard University, University of Maryland, Baltimore County, and the National Institutes of Health will train students to work in a collaborative team environment focused on addressing a pressing scientific problem. Realistic mathematical models can suggest best courses of intervention that can significantly reduce the number of HIV infections. The effect of the pre-exposure prophylaxis treatment (PrEP) will be included in a previously developed mathematical model of HIV. Previous models of imperfect vaccines have shown the potential for a backwards bifurcation that can dramatically affect the dynamics of the epidemic. As a result, the same intervention that brings a model without a vaccine to the disease-free equilibrium, could drive the dynamics of the model with PrEP to a stable endemic equilibrium. Transmission of HIV depends on the viral-load of the infected individual. Thus, realistic mathematical models must include the effect of non-steady highly active anti-retroviral treatment (HAART) through structured treatment interruptions, lack of adherence to drug regimen and drug resistance. Non-steady HAART treatment regimes and the subsequent two-way movement between virally suppressed and chronically infected will require using non-exponential treatment stages into the model, which will be fitted to publicly available Multicenter AIDS Cohort Study (MACS) data from the Johns Hopkins Bloomberg School of Public Health. Since public health data will be used in the mathematical model, parameter identifiability will be addressed structurally and practically. Several numerical tools for accessing structural identifiability of the model will be used. The profile likelihood method will be used to assess the practical identifiability of model parameters and to provide confidence intervals for parameter estimation. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.